The organisation, whose ostensible goal is to set up a separate Islamic nation within the Philippines, is believed to have organisational and financial links with al Qaeda, fed by Islamic charities and the proceeds of kidnapping foreigners.
Individual cases only support this thesis. Ramzi Yousef, convicted ringleader of the 1993 attempt to blow up the World Trade Center in New York, plotted in Manila to blow up 11 jumbo jets en route to the US, while one of the men convicted of the 1998 US Embassy bombing in Kenya was a student in the Philippines when he was recruited into the bin Laden organisation.
This month, President Gloria Arroyo herself acknowledged that there were "traces of a relationship" between Abu Sayyaf and the group which planned the September 11 attacks in New York and Washington. US intelligence experts describe Manila as a "major operational hub" of al Qaeda in its "holy war" against America.
For the public record, Filipino officials rule out any direct participation by US forces to root out the guerrillas, which would in any case be barred by the country's constitution. But as a host of precedents - from Vietnam and earlier - show, US trainers and advisers can very swiftly metamorphose into full-scale combatants by another name. The US moreover will be able to use its two former major installations in the Philippines, at Clark Air Base and Subic Bay, as bases for its operations.
The pattern is similar in Indonesia, where Islamic forces have been involved in some of the separatist violence which has long racked it.
Though Indonesian Muslims are mostly moderate, there are extremist militias believed to be linked with bin Laden's organisation.
One such group, Darul Islam, has owned up to having links with al Qaeda and the Taleban regime.
"Some factions in Darul Islam have had close contact with the al Qaeda movement and close contact with persons in Afghanistan," the group's spokesman Al Chaidar said.
"They have, several times, invited Osama bin Laden to Indonesia. But Osama, himself, has not had a chance to go to Indonesia."
A number of fringe Islamic groups have threatened to round up and expel Americans and other Westerners and have demanded that the country oppose the bombing of Afghanistan.
Though by the standards of street protest in Indonesia, the demonstrations against the US air strikes on Afghanistan have been on a small scale, they have been passionate and highly visible.
Students have protested outside Parliament in Jakarta, burning effigies of Bush and accusing America of terrorism and of conducting a war against all of Islam.
Malaysia is also involved. Al Qaeda suspects have used Kuala Lumpur Airport, and Khalid Al-Midhar, one of the hijackers of the American Airlines jet which was crashed into the Pentagon and who was already on a US Government watchlist of suspected terrorists, was videotaped at a terrorist meeting in the Malaysian capital last year.
The message from US officials is that all three of these countries - and by implication anywhere else where such al Qaeda cells may exist - could be the target of covert operations, carried out in collaboration with local security forces, or in exceptional cases by US special forces.
Bush himself will discuss the problem with their three leaders next week at the Asia Pacific Economic Cooperation summit in Shanghai.
But intelligence sources in Britain say the previously unappreciated danger of al Qaeda comes in the widely dispersed way it had set up bases internationally.
There are al Qaeda cells or associated terror groups in Algeria and Egypt, Chechnya, Turkmenistan and Uzbekistan, and in South America.
Cells are also believed to be active in Kenya, Somalia, Tanzania and possibly South Africa.
The intelligence source said: "They appear to have a policy of sending recruits away for training [to Afghanistan] so they escape the attention of their domestic security services.
"Afterwards they are dispersed to unlikely places like the Philippines again, so that they are away from the microscope of interested law enforcement agencies.
"It's almost like an international conglomerate in the way it moves its members around.
"There is a Pan-Islamic nature to the organisation - look at the multinational make-up of the 19 hijackers who attacked America. Recruits are told their loyalty lies not just to fellow Muslims in their country of origin but Muslims everywhere".
Al Qaeda members have also been spotted in northern Kosovo. There is unconfirmed evidence that bin Laden's group had plotted to carry out an attack on the US Embassy in New Delhi.
Colin Powell, the Secretary of State, said yesterday that: "This war will never really stop in any of its phases - military, diplomatic and financial."
Even as the plumes of smoke still hang in the air over Kabul and Kandahar, the realisation is sinking in. The US is in it for the long haul, across the global board.
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INDEPENDENT
Map: Opposing forces in the war against terror
Afghanistan facts and links
Full coverage: Terror in America
